Question: Solve for $x$ and $y$ using substitution. ${-x-5y = 7}$ ${x = -y-3}$
Since $x$ has already been solved for, substitute $-y-3$ for $x$ in the first equation. ${-}{(-y-3)}{- 5y = 7}$ Simplify and solve for $y$ $y+3 - 5y = 7$ $-4y+3 = 7$ $-4y+3{-3} = 7{-3}$ $-4y = 4$ $\dfrac{-4y}{{-4}} = \dfrac{4}{{-4}}$ ${y = -1}$ Now that you know ${y = -1}$ , plug it back into $\thinspace {x = -y-3}\thinspace$ to find $x$ ${x = -}{(-1)}{ - 3}$ $x = 1 - 3$ ${x = -2}$ You can also plug ${y = -1}$ into $\thinspace {-x-5y = 7}\thinspace$ and get the same answer for $x$ : ${-x - 5}{(-1)}{= 7}$ ${x = -2}$